New expressions for the pdf and cdf of the filtered output of an analog cross correlator (Corresp.)

A general expression is derived for the probability density function (pdf) associated with the filtered output of an analog cross correlator, the inputs of which consist of deterministic signals having the same frequency plus correlated stationary Gaussian noise processes. The correlator is composed of input bandpass filters, a multiplier, and a zonal Iowpass filter. The noise components in each channel have distinct variances and obey no spectral symmetry condition. Using the derived expression for the pdf, the cumulative distribution function (cdf) under the same general conditions is calculated. All previous known special cases are subsequently deduced from the general expressions given here. The general results derived here are more suitable for numerical computations than comparable previous results found in the literature due to the fact that expressions here do not involve multiple infinite series. Lastly, asymptotic formulas are developed for both the pdf and cdf which may be helpful in certain calculations.